This paper introduces a review on directed information and its application as a causality measure among two stochastic processes. Jiao's method for estimating directed information from data, using the context tree weighting algorithm is described and then used to infer synaptic connectivity from simulated neurons, from their neural spike trains only. It is observed that positive values of directed information estimates correctly predicted synaptic connections.

The relation between physical stimuli and neurophysiological responses, such as action potentials (spikes) and Local Field Potentials (LFP), has recently been experimented in order to explain how neurons encode auditory information. However, none of these experiments presented analyses with postsynaptic potentials (PSPs). In the present study, we have estimated information values between auditory stimuli and amplitudes/latencies of PSPs and LFPs in anesthetized rats in vivo. To obtain these values, a new method of information estimation was used. This method produced more accurate estimates than those obtained by using the traditional binning method; a fact that was corroborated by simulated data. The traditional binning method could not certainly impart such accuracy even when adjusted by quadratic extrapolation. We found that the information obtained from LFP amplitude variation was significantly greater than the information obtained from PSP amplitude variation. This confirms the fact that LFP reflects the action of many PSPs. Results have shown that the auditory cortex codes more information of stimuli frequency with slow oscillations in groups of neurons than it does with slow oscillations in neurons separately.

This paper introduces the use of a directed information estimator for discrete-valued processes to continuousvalued processes by previously discretizing the continuous-valued processes according to three different and generally applicable methods. The directed information estimator uses context tree weighting algorithm (CTW). The three discretization methods are called equidistant, equipopulated and symbolic methods. Simulated results indicate that faster and more conservative results are found by using few discretization levels with equipopulated method.

Abstract-Transfer entropy is a measure of causality that has been widely applied and one of its identities is the sum of mutual information terms. In this article we evaluate two existing methods of mutual information estimation in the specific application of detecting causality between a discrete random process and a continuous random process: binning method and nearest neighbours method. Simulated examples confirm, in the overall scenario, that the nearest neighbours method detects causality more reliably than the binning method.

This research investigates the applicability of a relatively new estimator of mutual information, KSG estimator, to find the reconstruction delay of phase space in dynamical systems. There are evidences that the KSG estimator is more accurate than the naive method commonly used. Methods: In this paper we estimated mutual information between the voice signals and their delayed versions, with KSG method. The voice signals were obtained from a disordered voice database. Then, we found the reconstruction delay where mutual information reached its first minimum. We applied the encountered value of reconstruction delay in linear discriminant analysis, in order to discriminate between healthy and pathological voices or to discriminate between pathologies. Discrimination between voice pathologies using nonlinear measurements is still not much explored. Moreover, in this paper we used a single nonlinear measurement: reconstruction delay. Results: The results show that the reconstruction delay obtained with KSG method has increased classification rates in most cases, in terms of accuracy, sensitivity and specificity, when compared to the naive estimator usually adopted. Conclusion: The KSG estimator is a promising technique to improve the diagnosis of voice related pathologies.